> anova(lm(SUGARS ~ factor(SHELF) + (FAT>0)))
Analysis of Variance Table

Response: SUGARS
              Df  Sum Sq Mean Sq F value    Pr(>F)    
factor(SHELF)  2  248.41 124.204  8.0540 0.0006908 ***
FAT > 0        1  127.36 127.364  8.2589 0.0053083 ** 
Residuals     73 1125.76  15.421                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> interaction.plot(factor(SHELF), FAT>0, SUGARS)
> anova(lm(SUGARS ~ factor(SHELF) + (FAT>0) + factor(SHELF)*(FAT>0)))
Analysis of Variance Table

Response: SUGARS
                      Df  Sum Sq Mean Sq F value    Pr(>F)    
factor(SHELF)          2  248.41 124.204  8.1359 0.0006587 ***
FAT > 0                1  127.36 127.364  8.3428 0.0051297 ** 
factor(SHELF):FAT > 0  2   41.86  20.929  1.3709 0.2605117    
Residuals             71 1083.90  15.266                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> lm(CALORIES ~ SUGARS)

Call:
lm(formula = CALORIES ~ SUGARS)

Coefficients:
(Intercept)       SUGARS  
     89.820        2.465  

> plot(CALORIES ~ SUGAR)
Error in eval(expr, envir, enclos) : object 'SUGAR' not found
> plot(CALORIES ~ SUGARS)
> plot(lm(CALORIES ~ SUGAR))
Error in eval(expr, envir, enclos) : object 'SUGAR' not found
> plot(lm(CALORIES ~ SUGARS))
Hit <Return> to see next plot: 
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> cereal[c(55,56),]
           NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
55  Puffed_Rice       50       1   0      0     0    13      0     3
56 Puffed_Wheat       50       2   0      0     1    10      0     3
> summary(lm(CALORIES ~ SUGARS))

Call:
lm(formula = CALORIES ~ SUGARS)

Residuals:
     Min       1Q   Median       3Q      Max 
-39.8201  -9.4003   0.4598  12.6449  38.1347 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  89.8201     3.4366  26.137  < 2e-16 ***
SUGARS        2.4650     0.4185   5.889 1.02e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.22 on 75 degrees of freedom
Multiple R-squared: 0.3162,	Adjusted R-squared: 0.3071 
F-statistic: 34.69 on 1 and 75 DF,  p-value: 1.025e-07 

> plot(lm(CALORIES ~ SUGARS + FAT))
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> cereal[2,]
               NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
2 100%_Natural_Bran      120       3   5     15     2     8      8     3
> summary(lm(CALORIES ~ SUGARS + FAT))

Call:
lm(formula = CALORIES ~ SUGARS + FAT)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.5623  -7.0534   0.2883   9.7544  33.6903 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  85.5623     3.2792  26.092  < 2e-16 ***
SUGARS        2.0213     0.3941   5.129 2.26e-06 ***
FAT           7.2349     1.7406   4.157 8.58e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 14.7 on 74 degrees of freedom
Multiple R-squared: 0.4457,	Adjusted R-squared: 0.4307 
F-statistic: 29.75 on 2 and 74 DF,  p-value: 3.31e-10 

> summary(lm(CALORIES ~ SUGARS))

Call:
lm(formula = CALORIES ~ SUGARS)

Residuals:
     Min       1Q   Median       3Q      Max 
-39.8201  -9.4003   0.4598  12.6449  38.1347 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  89.8201     3.4366  26.137  < 2e-16 ***
SUGARS        2.4650     0.4185   5.889 1.02e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.22 on 75 degrees of freedom
Multiple R-squared: 0.3162,	Adjusted R-squared: 0.3071 
F-statistic: 34.69 on 1 and 75 DF,  p-value: 1.025e-07 

> summary(lm(CALORIES ~ SUGARS + FAT))

Call:
lm(formula = CALORIES ~ SUGARS + FAT)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.5623  -7.0534   0.2883   9.7544  33.6903 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  85.5623     3.2792  26.092  < 2e-16 ***
SUGARS        2.0213     0.3941   5.129 2.26e-06 ***
FAT           7.2349     1.7406   4.157 8.58e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 14.7 on 74 degrees of freedom
Multiple R-squared: 0.4457,	Adjusted R-squared: 0.4307 
F-statistic: 29.75 on 2 and 74 DF,  p-value: 3.31e-10 

> summary(lm(CALORIES ~ SUGARS))

Call:
lm(formula = CALORIES ~ SUGARS)

Residuals:
     Min       1Q   Median       3Q      Max 
-39.8201  -9.4003   0.4598  12.6449  38.1347 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  89.8201     3.4366  26.137  < 2e-16 ***
SUGARS        2.4650     0.4185   5.889 1.02e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 16.22 on 75 degrees of freedom
Multiple R-squared: 0.3162,	Adjusted R-squared: 0.3071 
F-statistic: 34.69 on 1 and 75 DF,  p-value: 1.025e-07 

> summary(lm(CALORIES ~ SUGARS + FAT))

Call:
lm(formula = CALORIES ~ SUGARS + FAT)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.5623  -7.0534   0.2883   9.7544  33.6903 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  85.5623     3.2792  26.092  < 2e-16 ***
SUGARS        2.0213     0.3941   5.129 2.26e-06 ***
FAT           7.2349     1.7406   4.157 8.58e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 14.7 on 74 degrees of freedom
Multiple R-squared: 0.4457,	Adjusted R-squared: 0.4307 
F-statistic: 29.75 on 2 and 74 DF,  p-value: 3.31e-10 

> confint(lm(CALORIES ~ SUGARS + FAT))
                2.5 %    97.5 %
(Intercept) 79.028318 92.096269
SUGARS       1.236037  2.806662
FAT          3.766746 10.703102
> cereal[1,]
       NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
1 100%_Bran       70       4   1    130    10     5      6     3
> plot(lm(CALORIES ~ SUGARS + FAT + PROTEIN))
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> summary(lm(CALORIES ~ SUGARS + FAT + PROTEIN))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + PROTEIN)

Residuals:
     Min       1Q   Median       3Q      Max 
-37.8457  -7.0108  -0.2365   8.8708  32.1679 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  79.5344     5.9680  13.327  < 2e-16 ***
SUGARS        2.2343     0.4307   5.188 1.84e-06 ***
FAT           6.5091     1.8364   3.544  0.00069 ***
PROTEIN       2.0778     1.7211   1.207  0.23122    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 14.66 on 73 degrees of freedom
Multiple R-squared: 0.4565,	Adjusted R-squared: 0.4342 
F-statistic: 20.44 on 3 and 73 DF,  p-value: 1.021e-09 

> plot(lm(CALORIES ~ SUGARS + FAT + FIBER))
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> cereal[1:4,]
                       NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
1                 100%_Bran       70       4   1    130    10     5      6     3
2         100%_Natural_Bran      120       3   5     15     2     8      8     3
3                  All-Bran       70       4   1    260     9     7      5     3
4 All-Bran_with_Extra_Fiber       50       4   0    140    14     8      0     3
> summary(lm(CALORIES ~ SUGARS + FAT + FIBER))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + FIBER)

Residuals:
     Min       1Q   Median       3Q      Max 
-40.6531  -9.8873  -0.1173   7.1988  36.0890 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  90.6531     3.5962  25.208  < 2e-16 ***
SUGARS        1.8558     0.3805   4.877 6.11e-06 ***
FAT           7.5106     1.6638   4.514 2.39e-05 ***
FIBER        -1.9630     0.6832  -2.873  0.00532 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 14.03 on 73 degrees of freedom
Multiple R-squared: 0.502,	Adjusted R-squared: 0.4815 
F-statistic: 24.53 on 3 and 73 DF,  p-value: 4.403e-11 

> cereal[1:4,]
                       NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
1                 100%_Bran       70       4   1    130    10     5      6     3
2         100%_Natural_Bran      120       3   5     15     2     8      8     3
3                  All-Bran       70       4   1    260     9     7      5     3
4 All-Bran_with_Extra_Fiber       50       4   0    140    14     8      0     3
> plot(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN))
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> summary(lm(CALORIES ~ SUGARS + FAT + FIBER + PROTEIN))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + FIBER + PROTEIN)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.3305  -8.2901   0.4364   8.3081  33.2686 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  76.7918     5.4020  14.215  < 2e-16 ***
SUGARS        2.3543     0.3881   6.066 5.52e-08 ***
FAT           5.6355     1.6631   3.389  0.00114 ** 
FIBER        -3.1632     0.7381  -4.286 5.56e-05 ***
PROTEIN       5.8509     1.7799   3.287  0.00157 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.17 on 72 degrees of freedom
Multiple R-squared: 0.567,	Adjusted R-squared: 0.5429 
F-statistic: 23.57 on 4 and 72 DF,  p-value: 1.76e-12 

> summary(lm(CALORIES ~ SUGARS + FAT + PROTEIN+ FIBER ))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + PROTEIN + FIBER)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.3305  -8.2901   0.4364   8.3081  33.2686 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  76.7918     5.4020  14.215  < 2e-16 ***
SUGARS        2.3543     0.3881   6.066 5.52e-08 ***
FAT           5.6355     1.6631   3.389  0.00114 ** 
PROTEIN       5.8509     1.7799   3.287  0.00157 ** 
FIBER        -3.1632     0.7381  -4.286 5.56e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.17 on 72 degrees of freedom
Multiple R-squared: 0.567,	Adjusted R-squared: 0.5429 
F-statistic: 23.57 on 4 and 72 DF,  p-value: 1.76e-12 

> plot(CALORIES ~ PROTEIN)
> summary(lm(CALORIES ~ SUGARS + FAT + PROTEIN+ FIBER ))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + PROTEIN + FIBER)

Residuals:
     Min       1Q   Median       3Q      Max 
-35.3305  -8.2901   0.4364   8.3081  33.2686 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  76.7918     5.4020  14.215  < 2e-16 ***
SUGARS        2.3543     0.3881   6.066 5.52e-08 ***
FAT           5.6355     1.6631   3.389  0.00114 ** 
PROTEIN       5.8509     1.7799   3.287  0.00157 ** 
FIBER        -3.1632     0.7381  -4.286 5.56e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.17 on 72 degrees of freedom
Multiple R-squared: 0.567,	Adjusted R-squared: 0.5429 
F-statistic: 23.57 on 4 and 72 DF,  p-value: 1.76e-12 

> cereal[1:4,]
                       NAME CALORIES PROTEIN FAT SODIUM FIBER CARBO SUGARS SHELF
1                 100%_Bran       70       4   1    130    10     5      6     3
2         100%_Natural_Bran      120       3   5     15     2     8      8     3
3                  All-Bran       70       4   1    260     9     7      5     3
4 All-Bran_with_Extra_Fiber       50       4   0    140    14     8      0     3
> summary(lm(CALORIES ~ SUGARS + FAT + PROTEIN+ FIBER + SODIUM ))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + PROTEIN + FIBER + SODIUM)

Residuals:
     Min       1Q   Median       3Q      Max 
-26.8788  -7.6598  -0.3427   7.0683  34.2768 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 68.40442    5.66573  12.073  < 2e-16 ***
SUGARS       2.23748    0.36559   6.120 4.60e-08 ***
FAT          5.81734    1.56023   3.729 0.000384 ***
PROTEIN      5.75375    1.66903   3.447 0.000955 ***
FIBER       -3.03308    0.69314  -4.376 4.07e-05 ***
SODIUM       0.05623    0.01703   3.303 0.001501 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 12.35 on 71 degrees of freedom
Multiple R-squared: 0.6246,	Adjusted R-squared: 0.5982 
F-statistic: 23.63 on 5 and 71 DF,  p-value: 6.629e-14 

> summary(lm(CALORIES ~ SUGARS + FAT + PROTEIN+ FIBER + SHELF ))

Call:
lm(formula = CALORIES ~ SUGARS + FAT + PROTEIN + FIBER + SHELF)

Residuals:
     Min       1Q   Median       3Q      Max 
-36.5804  -7.3538   0.4826   7.6918  32.8009 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  74.8914     6.5128  11.499  < 2e-16 ***
SUGARS        2.3434     0.3906   5.999 7.55e-08 ***
FAT           5.4108     1.7247   3.137  0.00248 ** 
PROTEIN       5.9068     1.7920   3.296  0.00153 ** 
FIBER        -3.2868     0.7779  -4.225 6.98e-05 ***
SHELF         1.0540     1.9952   0.528  0.59894    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 13.24 on 71 degrees of freedom
Multiple R-squared: 0.5687,	Adjusted R-squared: 0.5383 
F-statistic: 18.72 on 5 and 71 DF,  p-value: 8.055e-12 

>